Das-Gupta-Type Contraction Mapping Theorems in (α, β) - Complex Valued b-Metric Spaces
DOI:
https://doi.org/10.33003/fjs-2026-1015-4067Keywords:
Fixed Point, B-Metric Space, Complex-Valued Metric Space, (α, β)-Complex Valued b-Metric Space, Das-Gupta Contraction, Rational MappingAbstract
In this paper, we investigate fixed-point problems for a class of Das–Gupta-type rational contraction mappings defined on complete (α, β)-complex-valued b-metric spaces. We establish the existence and uniqueness of a fixed point. The proof is based on the Picard iterative sequence, estimates for successive iterates, the generalized triangle inequality, and completeness of the underlying space. The additional parameter restriction is essential for the geometric-series argument used to establish the Cauchy property of the iterative sequence. The result provides a sufficient fixed-point criterion that extends the study of rational contractions to the (α, β)-complex-valued (b)-metric setting.
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Copyright (c) 2026 Abba Auwalu, Hassan Hamza
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